Download Chapter 2 - CP Physics

Dr. Dan Lawrence
PHYS 1110 Lectures
Lecture 25
Fluid Motion
Fluids in Motion:
Streamline Flow
• Streamline flow
– Every particle that passes a particular point moves
exactly along the smooth path followed by
particles that passed the point earlier
– Also called laminar flow
• Streamline is the path
– Different streamlines cannot cross each other
– The streamline at any point coincides with the
direction of fluid velocity at that point
Section 9.7
Streamline Flow, Example
• Streamline flow shown around an auto in a wind
tunnel
Section 9.7
Fluids in Motion:
Turbulent Flow
• The flow becomes irregular
– Exceeds a certain velocity
– Any condition that causes abrupt changes in
velocity
• Eddy currents are a characteristic of turbulent
flow
Section 9.7
Turbulent Flow, Example
• The smoke first moves
in laminar flow at the
bottom
• Turbulent flow occurs at
the top
Section 9.7
Fluid Flow: Viscosity
• Viscosity is the degree of internal friction in
the fluid
• The internal friction is associated with the
resistance between two adjacent layers of the
fluid moving relative to each other
Section 9.7
Characteristics of an Ideal Fluid
• The fluid is nonviscous
– There is no internal friction between adjacent layers
• The fluid is incompressible
– Its density is constant
• The fluid motion is steady
– The velocity, density, and pressure at each point in the fluid do
not change with time
• The fluid moves without turbulence
– No eddy currents are present
– The elements have zero angular velocity about its center
Section 9.7
Equation of Continuity
• A1v1 = A2v2
• The product of the
cross-sectional area of a
pipe and the fluid speed
is a constant
– Speed is high where the
pipe is narrow and speed
is low where the pipe
has a large diameter
• The product Av is called
the flow rate
Section 9.7
Equation of Continuity, cont
• The equation is a consequence of conservation of
mass and a steady flow
• A v = constant
– This is equivalent to the fact that the volume of fluid that
enters one end of the tube in a given time interval equals
the volume of fluid leaving the tube in the same interval
• Assumes the fluid is incompressible and there are no leaks
Section 9.7
Each second, 5,525 m3 of water flows over the 670 m wide cliff of the
Horseshoe Falls portion of Niagara Falls. The water is approximately
2 m deep as it reaches the cliff. What is its speed at that instant?
Daniel Bernoulli
• 1700 – 1782
• Swiss physicist and
mathematician
• Wrote Hydrodynamica
• Also did work that was
the beginning of the
kinetic theory of gases
Section 9.7
Bernoulli’s Equation
• Relates pressure to fluid speed and elevation
• Bernoulli’s equation is a consequence of
Conservation of Energy applied to an ideal fluid
• Assumes the fluid is incompressible and nonviscous,
and flows in a nonturbulent, steady-state manner
Section 9.7
Bernoulli’s Equation, cont.
• States that the sum of the pressure, kinetic
energy per unit volume, and the potential
energy per unit volume has the same value at
all points along a streamline
1 2
P + rv + r gh = Constant
2
Section 9.7
A large pipe with a cross-sectional area of 1.00 m2 descends 5.00 m and
narrows to 0.500 m2, where it terminates in a valve. If the pressure at point 2
is atmospheric pressure, and the valve is opened wide and the water allowed
to flow freely, find the speed of the water leaving the pipe.
A woodpecker pecks a hold in an old wooden water tank. If the top of the tank
is open to the atmosphere, determine the speed of the water leaving the hole
if the water level is 0.500 m above the hole. How far away does the water hit
the ground if the hole is 3.00 m above the ground?
Applications of Bernoulli’s Principle:
Measuring Speed
• Shows fluid flowing
through a horizontal
constricted pipe
• Speed changes as
diameter changes
• Can be used to measure
the speed of the fluid
flow
• Swiftly moving fluids
exert less pressure than
do slowly moving fluids
Section 9.7
Applications of Bernoulli’s Principle:
Venturi Tube
• The height is higher in
the constricted area of
the tube
• This indicates that the
pressure is lower
Section 9.7
An Object Moving Through a Fluid
• Many common phenomena can be explained by
Bernoulli’s equation
– At least partially
• In general, an object moving through a fluid is acted
upon by a net upward force as the result of any
effect that causes the fluid to change its direction as
it flows past the object
• Swiftly moving fluids exert less pressure than do
slowing moving fluids
Section 9.8
Application – Golf Ball
• The dimples in the golf
ball help move air along
its surface
• The ball pushes the air
down
• Newton’s Third Law tells
us the air must push up
on the ball
• The spinning ball travels
farther than if it were not
spinning
Section 9.8
Application – Atomizer
• A stream of air passing
over an open tube
reduces the pressure
above the tube
• The liquid rises into the
airstream
• The liquid is then
dispersed into a fine
spray of droplets
Section 9.8
Application – Vascular Flutter
• The artery is constricted
as a result of accumulated
plaque on its inner walls
• To maintain a constant
flow rate, the blood must
travel faster than normal
• If the speed is high
enough, the blood
pressure is low and the
artery may collapse
Section 9.8
Application – Airplane Wing
• The air speed above the
wing is greater than the
speed below
• The air pressure above
the wing is less than the
air pressure below
• There is a net upward
force
– Called lift
• Other factors are also
involved
An airplane’s wings each have an area of 4.0 m2. When flying level, the
speed of the air over the wings is 245 m/s, while the speed of the air
under the wings is 222 m/s. What is the mass of the plane?
Review
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Streamline Flow
Turbulent Flow
Continuity Equation
Bernoulli’s Equation